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- W3083500111 abstract "In this paper we show that all algebro-geometric finite gap solutions to the Korteweg–de Vries equation can be realized as a limit of N-soliton solutions as N diverges to infinity (see remark 1 for the precise meaning of this statement). This is done using the primitive solution framework initiated by Dyachenko et al. (2016) and Zakharov et al. (2016) [25, 26]. One implication of this result is that the N-soliton solutions can approximate any bounded periodic solution to the Korteweg–de Vries equation arbitrarily well in the limit as N diverges to infinity. We also study primitive solutions numerically that have the same spectral properties as the algebro-geometric finite gap solutions but are not algebro-geometric solutions." @default.
- W3083500111 created "2020-09-11" @default.
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- W3083500111 date "2020-12-01" @default.
- W3083500111 modified "2023-10-02" @default.
- W3083500111 title "Algebro-geometric finite gap solutions to the Korteweg–de Vries equation as primitive solutions" @default.
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- W3083500111 doi "https://doi.org/10.1016/j.physd.2020.132709" @default.
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